On Pillai's problem involving two linear recurrent sequences : Padovan and Fibonacci

Abstract

In this paper, we find all integers $c$ having at least two representations as a difference between linear recurrent sequences. This problem is a pillai problem involving Padovan and Fibonacci sequence. The proof of our main theorem uses lower bounds for linear forms in logarithms, properties of continued fractions, and a version of the Baker-Davenport reduction method in Diophantine approximation.

arXiv admin note: text overlap with arXiv:1902.03491 by other authors

References in corpus (2)

• On a problem of Pillai with Fibonacci numbers and powers of 2
• On solutions of the Diophantine equation $L_n+L_m=3^a$